Enthalpy calculator

ABSTRACT

An enthalpy calculator outputs a value of enthalpy directly calculated from two measured items such as dry bulb temperature and relative humidity, and includes: a humidity sensor for converting relative humidity into an electrical signal; a temperature sensor for converting dry bulb temperature into an electrical signal; and arithmetic units for outputting the calculated enthalpy value as an electrical signal after performing a calculation based on the signals input by the temperature sensor 12 and the humidity sensor 5 in accordance with the following equation: 
     
         i=atψ+bt+cψ+d 
    
     wherein 
     a, b, c, and d are preselected constants, and: 
     t: dry bulb temperature (°C.) 
     ψ: relative humidity (%), 
     a, b, c, and d being selected so that |i-i 0  |≦0.5 within a fixed temperature range if: 
     
         i.sub.0 =0.240t+(597.3+0.441t)x 
    
     and 
     
         x=0.622·ψ·h/P-ψ·h 
    
     wherein 
     P: atmospheric pressure (mmHg) around the output unit 
     h: saturated vapor pressure (mmHg) under atmospheric pressure P.

This application is a continuation-in-part of application Ser. No.532,023, filed Aug. 26, 1983, now abandoned.

BACKGROUND OF THE INVENTION

This invention relates to an enthalpy calculator in which the enthalpyof a body of gas or humid air is calculated by an arithmetic unit inaccordance with an enthalpy equation from the measured temperature andrelative humidity of the body of gas, and in which the calculated valueis converted into electrical signals which are output therefrom.

The enthalpy of humid air is obtained by the following equations (A) and(B) when the temperature and pressure thereof are within the ranges inwhich every-day air conditioning is carried out.

    i=0.240t+(597.3+0.441t)x                                   (A)

    x=0.622h.sub.s ·ψ/P-h.sub.s ·ψ   (B)

where

t: dry bulb temperature (°C.),

x: humidity ratio (kg/kg'),

P: atmospheric pressure (mmHg),

h_(s) : saturated vapor pressure (mmHg) at temperature t,

ψ: relative humidity (%),

i: enthalpy (Kcal/kg').

With equation (B), a complicated calculation is needed in which a valueobtained by an approximate expression that has hitherto been disclosed,such as the IFC Formulation for Industrial Use, must be substitutedtherein to obtain the saturated vapor pressure.

Accordingly, to obtain a value for the enthalpy of humid air using aconventional arithmetic unit it has been necessary to find the value ofone other factor, in addition to the dry bulb temperature, as a measuredvalue. That is to say, conventional methods depend on the humidityratio, wet bulb temperature, relative humidity, and dew pointtemperature and, whichever method is used, the values measured areconverted into enthalpy in accordance with equations (A) and (B) usingan electronic computer. Any method depending on finding the dew pointtemperature or the humidity ratio has the drawbacks of the slow reactionspeed and expensive sensing elements, and other methods depending on thewet bulb temperature, relative humidity, and dew point temperature havea disadvantage in that the solving of complicated equations arerequired.

SUMMARY OF THE INVENTION

According to this invention, the value of enthalpy is given by anarithmetic unit performing calculations using the following enthalpycalculation equations (C) and (D), which consist of a sum of the productof a linear function of the dry bulb temperature multiplied by a linearfunction of the relative humidity, and constants, the dry bulbtemperature and the relative humidity being important elements in theair-conditioning of the environment, when a limitation is imposed on therange of temperature (about 20°-30° C.) of air in a room when healthyair conditioning is provided.

    i=a·t·ψ+b·t+c·ψ+d (C)

    i=a(t+P)·(ψ+q)+r                              (D)

where a, b, c, d, P, q, and r are all constants.

By using equations (C) and (D) according to this invention, a value ofenthalpy which is more accurate than that read from a physchrometricdiagram can be found easily without performing the conventionalcomplicated calculations based on equations (A) and (B), provided thatthe temperature at which the enthalpy is calculated is within thetemperature range used in practice.

The method of deriving equations (C) or (D) will now be described. FIG.1 is a graph showing the values of enthalpy i calculated from apsychrometric diagram (i-x diagram) and the fundamental equations (A)and (B) for calculating enthalpy, with the condition that the dry bulbtemperature is kept constant. In this case, the enthalpy can beapproximated by a linear function of the relative humidity as expressedby equation (E) as follows:

    i=mψ+n                                                 (E)

where m and n are constants. If corrections to m and n at each degree oftemperature are examined, they can be expressed by approximateexpressions (F) and (G) which are linear functions of the temperature twithin a certain range temperature of t₁ to t₂, as follows:

    m=at+c                                                     (F)

    n=bt+d                                                     (G)

where a, b, c, and d are constants.

Therefore, by substituting equations (F) and (G) into equation (E),equations (C) and (D) can be obtained.

According to this invention, by measuring the dry bulb temperature andthe relative humidity, it is possible, within a certain range oftemperatures, to reduce the difference between the enthalpy valueobtained by the simple calculation expressed by equation (C) or (D) andthat obtained by the fundamental equations (A) and (B) to a minimum.

The following equation (H) provides values of the coefficients a, b, c,and d applied to the range of temperature from 20° to 30° C. usingequation (C), based on temperatures set at 22.5° and 27.5° C. andrelative humidities at 30 and 70%.

    i=7.616×10.sup.-3 ψ·t+0.2301t-0.06704ψ+0.1634 (H)

                  TABLE 1    ______________________________________    (kcal/kg')    i-i.sub.0    Relative Temperature (°C.)    humidity (%)             20      22      24    26    28    30    ______________________________________    10       -0.053  -0.036  -0.033                                   -0.044                                         -0.071                                               -0.116    20       -0.076  -0.024  0.002 -0.002                                         -0.039                                               -0.111    30       -0.102  -0.016  0.030 0.031 -0.018                                               -0.120    40       -0.133  -0.014  0.051 0.055 -0.007                                               -0.143    50       -0.168  -0.017  0.066 0.071 -0.008                                               -0.180    60       -0.208  -0.025  0.073 0.078 -0.020                                               -0.231    70       -0.251  -0.039  0.074 0.076 -0.043                                               -0.297    80       -0.298  -0.058  0.068 0.066 -0.077                                               -0.377    90       -0.350  -0.082  0.054 0.046 -0.12 -0.422    ______________________________________

In this case, using FIG. 1, the linear equations when t₃ =22.5° C. andt₄ =27.5° C., respectively, are:

    i=(0.104324338)ψ+5.3411041 (at t.sub.3)

    i=(0.142405671)ψ+6.49169099 (at t.sub.4)

Within the temperature range of t₃ to t₄ these values can be showngraphically as in FIGS. 2 and 3, to provide:

    m=7.616×10.sup.-3 t-0.06704

    n=0.2301t+0.1634.

Hence, the constants a through d are:

a=7.616×10⁻³

b=0.2301

c=-0.06704

d=0.1634

As shown in Table 1, the value of enthalpy i obtained from equation (H)is so accurate that the difference between it and that obtained from thefundamental equations (A) and (B) is at most 0.5 within the whole of thetemperature range of 20° to 30° C., this is sufficiently accurate forapplication within the range of temperatures and relative humiditiesused in practice. The temperature range on which the calculation isperformed can easily be changed by finding values for the constants inequations (C) and (D) afer changing the temperature range.

An arithmetic unit for performing the calculations based on equation (D)modified from equation (C) is composed of a multiplier for multiplyingthe linear function of temperature with that of relative humidity, bothof which having been converted into electrical signals, and of an adderfor summing the constants, so that a handy enthalpy calculation devicewhich outputs an electrical signal representing the enthalpy i can beobtained.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph of the relationship between relative humidity andenthalpy;

FIG. 2 is a graph of the relationship between dry bulb temperature andthe coefficient m;

FIG. 3 is a graph of the relationship between dry bulb temperature andthe coefficient n;

FIG. 4 is a block diagram of the composition of an embodiment of thisinvention;

FIG. 5 is a circuit diagram of an output unit in accordance with thepresent invention;

FIG. 6 is a circuit diagram of another example of an output unit inaccordance with the present invention;

FIGS. 7, 8, and 9 are circuit diagrams of other embodiments of thisinvention.

FIG. 10 is a basic configuration of another embodiment of the presentinvention.

FIG. 11 illustrates the temperature signal element 402 of FIG. 10.

FIG. 12 is a practical example of the basic configuration shown in FIG.11.

FIG. 13 shows a configuration of the humidity signal element 401illustrated in FIG. 11.

FIG. 14 illustrates the configuration of the temperature signal element402 of FIG. 11.

DESCRIPTION OF THE PREFERRED EMBODIMENT

A description will now be made of an embodiment of an enthalpycomputation unit performing calculations using equation (D), withreference to FIGS. 4 through 9.

FIG. 4 is a diagram of the basic composition of an arithmetic unit as anembodiment of this invention, wherein reference numeral 1 denotes ahumidity signal output section for outputting an voltage expressed by alinear function whose variable is the relative humidity; numeral 2denotes a temperature signal output section which changes the amplitudethereof in response to a resistance expressed by a linear functionwhosee variable is the temperature; and numeral 3 denotes a multiplierwhich multiplies the temperature output signal by the relative humidityoutput signal and outputs a value of enthalpy as a voltage which is fedto an output section 4.

In FIG. 5, numeral 5 indicates a humidity sensor which comprises aresistor 6 for sensing variations in humidity as variations in itselectrical resistance. The voltage at a terminal 7 is a value obtainedby dividing a voltage applied to a terminal 8 by the ratio of theresistances of humidity sensors 5 and 9, so that a linear function ofthe measured relative humidity is established. This comprises thehumidity signal output section 1. Numeral 10 denotes an operationalamplifier in which, when a voltage expressed as a linear function ofrelative humidity is input to an inverting input terminal thereof, avoltage is output from a terminal 14 in response to the amplificationdetermined by the combined resistance of a resistor 11 and a thermistor12. The thermistor 12 is a temperature sensor with a large B constant,and makes up the temperature signal output section 2 expressed by thelinear function whose variable is temperature. The voltage output fromthe terminal 14 is a product of the linear function whose variable isrelative humidity multiplied by the other linear function whose variableis temperature. The output section 4 is a summation section for summingthe constants of the approximate expression (D) and for adding thevoltages at terminals 14 and 16 by using an operational amplifier 15 asan adder. As a result, a value of the enthalpy expressed by theapproximate expression (D) is output from a terminal 17 as a voltage.

FIG. 6 shows another example of a humidity signal output section inaccordance with the present invention. Numeral 18 indicates anoscillation circuit, in which, by connecting a capacitor 19 for sensinghumidity variations as variations in its electrostatic capacity to theinput side of an inverting input terminal of an operational amplifier20, a frequency which is inversely proportional to the capacity of thecapacitor 19 and that of a resistor 22 is generated from an outputterminal 21 of the operational amplifier 20. Numeral 23 represents afrequency-voltage conversion section in which a collector current at acertain voltage is passed through a transistor 24 only when thepotential at terminal 21 is high, so as to charge and smooth the voltageof capacitors 25 and 26, and, at the same time, the charge on thecapacitors is discharged by a resistor 27 connected parallel to thecapacitor 26 so that the potential at capacitor 26 is proportional tothe frequency. Furthermore, a voltage which has been smoothed by passingit through a filter 28 is output from a terminal 29. Numeral 30indicates a correction section for correcting the voltage output fromthe frequency-voltage conversion section 23, so as to output the voltagerequired for the calculation from a terminal 31.

FIG. 7 shows another embodiment of this invention in which referencecharacter A denotes a relative humidity signal output section whichoutputs a constant rectangular-wave whose frequency is inverselyproportional to the capacity of a capacitor 107 and the value of aresistor 108 from an output terminal 109 of an operational amplifier 106when the capacitor 107 is connected to a non-inverting input of theoperational amplifier 106, and when the resistor 108 is connected by anegative feedback circuit. When the potential at terminal 109 is high, acollector current at a certain voltage flows through a transistor 110 tocharge a capacitor 111 which senses humidity variations as variations inits electrostatic capacity as well as charging and smoothing a voltageof a capacitor 112. The discharge of the stored charge is performed by aresistor 113 to the capacitor 112 and, as a result, the potential at aterminal 114 is proportional to the capacity of the capacitor 111. Inother words, the potential at terminal 114 is expressed by a linearfunction whose variable is relative humidity.

Reference character B indicates a temperature signal output section inwhich a combined resistance 115 consists of the resistance of a resistor116 sensing temperature variations as variations in resistance, and thepotential at a terminal 117 corresponds to a dividend obtained bydividing the voltage of the power source by the ratio of the combinedresistance 115 to the resistance of the resistor 118. That is, thepotential at terminal 117 can be expressed approximately as a linearfunction of the resistance 116, i.e., it varies with temperature.

Character C denotes a multiplication section comprising a FET 119 and anoperational amplifier 120, which multiplies the input voltages at theterminals 114 and 117 and outputs from a terminal 112a voltage amplifiedaccording to the amplification determined by a resistance 121 and FET119.

Character D indicates an addition section composed of an operationalamplifier 125 used as an adder for adding the voltage at terminal 122 toa voltage obtained by dividing the voltage of the power source by theratio of resistance between resistors 123 and 124, and for outputtingthe calculated enthalpy as a voltage from terminal 126.

FIG. 8 shows another embodiment of the present invention in whichnumeral 206 denotes a combined resistance composed of a resistor 207 forsensing temperature variations converted into voltage variations. Thevoltage at a terminal 208 is a value obtained by dividing the voltagebetween terminals 209 and 210 by the ratio of resistance 206 and 211,and can be expressed in terms of a linear function of the resistance ofresistor 207, i.e., temperature. An operational amplifier 212 is anin-phase amplifier in which, when the voltage expressed by the linearfunction of temperature is input to the non-inverting input terminalthereof, a voltage in response to the amplification determined by acombined resistance 215 comprising the resistance of a resistor 213, andthat of an other resistor 214 which senses relative humidity variationsas resistance variations, is output from a terminal 216. Assuming thatthe value of the combined resistance 215 is a resistance expressed by alinear function of relative humidity, the voltage at terminal 216 isthat obtained by the multiplication of the linear function oftemperature with that of relative humidity. An operational amplifier 217is an in-phase adder which outputs a voltage from a terminal 221 afteradding the voltage at terminal 216 to that at a terminal 220 which has apotential obtained by dividing the voltage between terminals 209 and 210by the ratio of resistances of resistors 218 and 219. The voltage at aterminal 221 corresponds to the calculated enthalpy expressed by the sumof the product of the linear functions of temperature and relativehumidity, and constants.

FIG. 9 shows still another embodiment of this invention, wherein numeral306 represents a combined resistance comprising a resistor 307 sensingrelative humidity variations as resistance variations. The voltage at aterminal 308 corresponds to a value obtained by dividing the voltagebetween resistors 306 and 311, and can be expressed by the resistance ofresistor 307, i.e., a linear function whose variable is relativehumidity. An operational amplifier 312 is an in-phase amplifier inwhich, when the voltage indicating the linear function is input to anon-inverting input terminal thereof, a voltage corresponding to theamplification determined by a combined resistance 315 comprising theresistance of a resistor 313 and that of a resistor 314 which sensestemperature variations as resistance variations, and by a constantvoltage output section 316, is output from a terminal 317.

Although it is possible to transform the value of the combinedresistance 315 into a resistance that can be expressed by the resistor314, i.e., a linear function of temperature, it is difficult to make theconstant terms agree with the values in equation (D) but, by providing aconstant voltage output section parallel to the resistor 315, agreementof the constant terms with their computed values is made easier.Therefore, the voltage at terminal 317 can be expressed as a product ofthe linear functions of temperature and relative humidity. Anoperational amplifier 318 is an in-phase adder for adding the voltagesat terminal 317 to that at a terminal 321 which has a potential obtainedby dividing the voltage between terminals 309 and 310 by the resistanceratio of resistors 319 and 320, and it outputs the calculated voltagefrom a terminal 322. That is to say, the voltage at terminal 322corresponds to an enthalpy value expressed as a sum of the product ofthe linear functions of temperature and relative humidity, and aconstant term.

FIG. 10 is a basic configuration of an embodiment according to anarithmetic formula (D), i=a(t+p) (ψ+q)+r, of the present invention,wherein element 401 denotes a humidity signal element which delivers ahumidity signal proportional to the relative humidity of a gas; element402 is a temperature signal element which delivers a temperature signalproportional to the humidity of said gas; element 405 is atemperature-humidity multiplying means which multiplies the temperaturesignal, humidity signal and constant a, and delivers a signalproportional to the product; element 406 is a humidity multiplying meanswhich delivers the product signal of the humidity signal value andconstant C; element 407 is a temperature multiplying means whichdelivers the product signal of the temperature signal value and constantb; element 408 is a constant setting means which delivers a signalcorresponding to constant d; element 409 is an adding means which addsup the outputs from said temperature-humidity multiplying means,humidity multiplying means, temperature multiplying means, and constantsetting means, and delivers a signal corresponding to the enthalpyvalue, and element 411 is an enthalpy calculating element which iscomposed of temperature-humidity multiplying means, temperaturemultiplying means, humidity multiplying means and constant settingmeans, and receives the temperature signal and the humidity signal, anddelivers a signal corresponding to the enthalpy value shown in formula(D).

In FIG. 11, the temperature signal element 402 in FIG. 10 is dividedinto a first temperature signal element 403 and a second temperaturesignal element 404. The purpose of this division is to form thetemperature-humidity multiplying means of a simple electronic circuit soas to easily obtain the product of the temperature signal, the humiditysignal, and the constant a.

FIG. 12 is a practical example of the basic configuration shown in FIG.11, wherein the temperature-humidity multiplying means 405 is awell-known inverting amplifier, being composed of input resistance R1,feedback resistance R2, and operational amplifier OP1. The relationshipbetween its output V₀ψt and input φ is expressed as v₀ψt =R₂ /R₁ ψ. Whena temperature sensing resistor element whose temperature coefficient isα and whose resistance at reference temperature is R₀ is used as thefeedback resistance R₂, since R₂ =R₀ (1+αt), the output v₀ψt of thetemperature-humidity multiplying means 405 is ##EQU1## where the firstterm αR₀ /R is the constant a in formula (D), and the second term is aterm proportional to the humidity value which has occurredsubordinately. As a result of generation of this term, the constant c ofthe humidity multiplying means becomes different from the constant c informula (D). This corrective formula is c'=c-R₀ /R₁. Here, by selectingthe constant of the humidity multiplying means 406 as c', the outputv₀ψt of the humidity multiplying means 406 corresponding to humiditysignal ψ is ##EQU2## The second terms of eqs. (1) and (2), which differsonly in the signs, are mutually canceled at the time of addition todetermine formula (D), and only the first terms of these two equationsare left over and added up. Constant c' is set in the degree ofamplification of the amplifier (not shown) which constitutes thehumidity product signal element 406. On the other hand, the temperaturemultiplying means 407 is an amplifier circuit composed of operationalamplifier OP2, input resistance R3 and feedback resistance R4, and therelationship of its output v_(0t) and input v_(t) is expressed as v_(0t)=R₄ /R₃ ·t. Therefore, the constant b can be set in the relationship ofb=R₄ /R₃. The constant setting means 408 is composed of the output partof the signal voltage corresponding to the constant D, dividing thereference voltage by the resistance, and the impedance converting part408a to convert the output impedance of its signal into a low impedance.

Finally, in the adding means 409, the signal outputs from saidtemperature-humidity multiplying means, humidity multiplying means,temperature multiplying means, and constant setting means are added up,and an output signal corresponding to the enthalpy value shown informula (D) is synthesized and delivered.

In the calculation of enthalpy value according to formula (D), it isrequired that the temperature signal t and humidity signal ψ beproportional to the temperature and humidity to be measured,respectively. Generating devices of humidity signal and temperaturesignal are shown in FIG. 13 and FIG. 14.

FIG. 13 shows a configuration of the humidity signal element 401,comprising a humidity detector 413, and a polygonal line approximatingelement 414, and a rectifying and smoothing element 415, and a biasadjusting element 416, and an amplifier 417. The humidity detector 413is a series circuit consisting of alternating-current power source 410,and a humidity sensing resistor element 411, and a temperature sensingresistor element 412, and the voltage across the temperature sensingresistor element 412 is picked up as a humidity signal. This temperaturesensing resistor element is intended to compensate for the temperaturecharacteristics of the humidity sensing resistor element. Incidentally,it is derived from the characteristics of the humidity sensing resistorelement that a humidity signal is taken from the temperature sensingresistor element which is connected in series to the humidity sensingresistor element 411. Because of the characteristics of the element,when the relative humidity of the atmosphere rises, the resistance ofthe element decreases. On the other hand, the necessary humidity signalis proportional to the relative humidity. A voltage of a requireddirection can be obtained from the terminal voltage of the temperaturesensing resistor element 412 connected in series to the humidity sensingresistor element 411. The humidity signal detected by the humiditydetector 413 is applied into the polygonal line approximating element414, where the relative humidity and relative humidity signal arecorrected into a linear function. The output of this polygonal lineapproximating element 414 is an alternating-current signal, which isconverted into a direct-current signal in the next stage of therectifying and smoothing element 415. The bias adjusting element 416 isthe zero point adjusting element of the humidity signal from therectifying and smoothing element 415, and as a result of thisadjustment, the humidity signal shows a value proportional to theambient relative humidity of the humidity sensing resistor element 411.

A practical example of the configuration of the temperature signalelement 402, is shown in FIG. 14. The temperature signal element 402consists of temperature detector 426 and amplifier 427, and it detectsthe ambient temperature, and delivers a temperature signal proportionalto it. The temperature detector 426 is composed of temperature sensingresistor element 421, and a parallel resistance 422, and a seriesresistance 423, and noise suppressing capacitors 424 and 425, and powersupplies V₁ and V₂. As the temperature sensing resistor element 421responds to the ambient temperature, its resistance varies, and atemperature signal proportional to the ambient temperature is delivered.This temperature signal is amplified in the amplifier 427, and anecessary temperature signal is obtained.

As has been described, an enthalpy output unit according to thisinvention uses a simple equation expressed as a sum of linear functionsof relative humidity and temperature, and a term of summed constants; iscapable of outputting a very accurate enthalpy value induced directlyand easily from two measured items such as temperature and relativehumidity; enables the construction of a circuit with only a fewcomponents; and enables a shift in the temperature range by analteration of the constants in the circuit, so that it can be utilizedover a wide range. The measured items required for the calculation arethe dry bulb temperature and the relative humidity which are the mostimportant factors for an index of environmental conditions and,accordingly, many advantages including the possibility of the directapplication thereof to air conditioning control is provided thereby.

What is claimed is:
 1. An enthalpy output device comprising: a humiditysensor for converting a relative humidity into an electrical signal; atemperature sensor for converting dry bulb temperature into anelectrical signal; a first multiplying means for multiplying saidelectrical signal of said humidity sensor by a first specified voltage;a second multiplying means for multiplying said electrical signal ofsaid temperature sensor by a second specified voltage; a thirdmultiplying means for multiplying said electrical signals of saidhumidity and temperature sensors together and for also multiplying theresult by a third specified voltage; a constant generating means forgenerating a fourth specified voltage, and an adding means for addingtogether said electrical signals of said first, second and thirdmultiplying means and said constant generating means; wherein an outputfrom said adding means is delivered as an enthalpy output.
 2. Anenthalpy output device as set forth in claim 1, wherein if said relativehumidity is ψ and said dry bulb temperature is t, then said first,second and third multiplying means, and said constant generating means,and said adding means together calculate a value equal to:

    7.616×10.sup.-3 ψt+0.2301t-0.06704ψ+0.1634.


3. An enthalpy output device comprising: a humidity sensor forconverting a relative humidity into an electrical signal; a temperaturesensor for converting a dry bulb temperature into an electrical signal;a first adding means for adding a first specified voltage to saidelectrical signal of said humidity sensor; a second adding means foradding a second specified voltage to said electrical signal of saidtemperature sensor; a multiplying means for multiplying said electricalsignals of said first and second adding means together and also formultiplying the result by a third specified voltage; a constantgenerating means for generating a fourth specified voltage, and a thirdadding means for adding together said electrical signals of saidmultiplying means and said constant generating means, wherein an outputfrom said third adding means is delivered as an enthalpy output.
 4. Anenthalpy output device as set forth in claim 3, wherein, if saidrelative humidity is ψ and said dry bulb temperature is t, then saidfirst, second and third adding means, and said constant generatingmeans, and said multiplying means together calculate a value equal to:##EQU3## wherein: a=7.616×10⁻³ b=0.2301 c=0.06704 d=0.1634.